Joint Estimation of Topology and Injection Statistics in Distribution Grids With Missing Nodes

Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This article discusses a theoretical framework to jointly estimate the operational topology and statistics of injections in radial distribution grids under limited availability of nodal voltage measurements. In particular, we show that our proposed algorithms are able to provably learn the exact grid topology and injection statistics at all unobserved nodes as long as they are not adjacent. The algorithm design is based on novel ordered trends in voltage magnitude fluctuations at node groups, that are independently of interest for radial physical flow networks. The complexity of the designed algorithms is theoretically analyzed and their performance is validated using both linearized and nonlinear ac power flow samples in test distribution grids.

[1]  Michael Chertkov,et al.  Exact Topology and Parameter Estimation in Distribution Grids with Minimal Observability , 2017, 2018 Power Systems Computation Conference (PSCC).

[2]  Michael Chertkov,et al.  Learning topology of distribution grids using only terminal node measurements , 2016, 2016 IEEE International Conference on Smart Grid Communications (SmartGridComm).

[3]  Murti V. Salapaka,et al.  Exact topology reconstruction of radial dynamical systems with applications to distribution system of the power grid , 2017, 2017 American Control Conference (ACC).

[4]  Vassilis Kekatos,et al.  Graph Algorithms for Topology Identification Using Power Grid Probing , 2018, IEEE Control Systems Letters.

[5]  A.G. Phadke,et al.  Power system frequency monitoring network (FNET) implementation , 2005, IEEE Transactions on Power Systems.

[6]  Ram Rajagopal,et al.  Feeder Topology Identification , 2015, ArXiv.

[7]  Saverio Bolognani,et al.  Identification of power distribution network topology via voltage correlation analysis , 2013, 52nd IEEE Conference on Decision and Control.

[8]  Steven H. Low,et al.  Convex relaxations and linear approximation for optimal power flow in multiphase radial networks , 2014, 2014 Power Systems Computation Conference.

[9]  Michael Chertkov,et al.  Structure Learning in Power Distribution Networks , 2015, IEEE Transactions on Control of Network Systems.

[10]  Michael Chertkov,et al.  Tractable structure learning in radial physical flow networks , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[11]  Vijay Arya,et al.  Inferring connectivity model from meter measurements in distribution networks , 2013, e-Energy '13.

[12]  Bin Yu,et al.  High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence , 2008, 0811.3628.

[13]  C. N. Liu,et al.  Approximating discrete probability distributions with dependence trees , 1968, IEEE Trans. Inf. Theory.

[14]  Michael Chertkov,et al.  Estimating distribution grid topologies: A graphical learning based approach , 2016, 2016 Power Systems Computation Conference (PSCC).

[15]  Naima Kaabouch,et al.  Cyber security in the Smart Grid: Survey and challenges , 2013, Comput. Networks.

[16]  S. Zampieri,et al.  On the Existence and Linear Approximation of the Power Flow Solution in Power Distribution Networks , 2014, IEEE Transactions on Power Systems.

[17]  Vincent Y. F. Tan,et al.  High-Dimensional Graphical Model Selection: Tractable Graph Families and Necessary Conditions , 2011, NIPS.

[18]  Kameshwar Poolla,et al.  Data-driven approach for distribution network topology detection , 2015, 2015 IEEE Power & Energy Society General Meeting.

[19]  Edmond Jonckheere,et al.  Statistical Structure Learning to Ensure Data Integrity in Smart Grid , 2015, IEEE Transactions on Smart Grid.

[20]  Michael Chertkov,et al.  Estimating topology and injection statistics in distribution grids with hidden nodes , 2017, 2017 IEEE International Conference on Smart Grid Communications (SmartGridComm).

[21]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[22]  Zhuo Lu,et al.  Cyber security in the Smart Grid: Survey and challenges , 2013, Comput. Networks.

[23]  Vincent Y. F. Tan,et al.  High-dimensional Gaussian graphical model selection: walk summability and local separation criterion , 2011, J. Mach. Learn. Res..

[24]  Blake Lundstrom,et al.  Learning Exact Topology of a Loopy Power Grid from Ambient Dynamics , 2017, e-Energy.

[25]  Michael I. Jordan,et al.  Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..

[26]  M. E. Baran,et al.  Optimal sizing of capacitors placed on a radial distribution system , 1989 .

[27]  Michael Chertkov,et al.  Topology Estimation Using Graphical Models in Multi-Phase Power Distribution Grids , 2018, IEEE Transactions on Power Systems.

[28]  R. Hoffman.  Practical State Estimation for Electric Distribution Networks , 2006, 2006 IEEE PES Power Systems Conference and Exposition.

[29]  Michael Chertkov,et al.  Learning topology of the power distribution grid with and without missing data , 2016, 2016 European Control Conference (ECC).

[30]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[31]  M. E. Baran,et al.  Optimal capacitor placement on radial distribution systems , 1989 .

[32]  Yang Weng,et al.  Urban Distribution Grid Topology Estimation via Group Lasso , 2016, ArXiv.

[33]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[34]  Miao He,et al.  A Dependency Graph Approach for Fault Detection and Localization Towards Secure Smart Grid , 2011, IEEE Transactions on Smart Grid.